How to know my permissions for bitbucket repo?

git bitbucket

As of today, Access Level is visible on the vertical panel on the right side of the Source/Master page of the repo. See this screenshot.

git bitbucket

The overview page shows your access level to a given repository.

git bitbucket

As per new bitbucket you see the permission details, once you click the 'clone' side menu.

Refer the screenshot

Note: As bitbucket tend to change UI multiple time(s), this answer may subject to not work for you. As of April'2020 UI was as given in screen shot.

CodeHunter